The ThreeME model

• Multi-sector Macroeconomic Model for the Evaluation of Environmental and Energy policy

• Macroeconomic multi-sector model with neo-keynesian features

  • Avoid the limitations of standard CGE models
    • Say something about the medium term (not only the long term)
    • More realistic results for policy makers
  • Similar dynamic and long term properties than the macroeconomic models used in Economic ministries and forecasting departments

• Open source model: www.threeme.org

  • To avoid usual criticisms on models: black-box, impossible to verify independently the results, too few users
  • Make application to other countries and by other institutions easier: EU, Mexico & Indonesia (AFD); Tunisia (UNEP), UK (OECD), Luxembourg (Statec), DG Trésor

Multisector model

• n sectors (e.g. France: n = 37; Tunisia: n = 21, Mexico: n = 29, Luxembourg: n = 26)

• Allows to analyze the effect of transfer of activities from one sector to another on:

  • Employment, due to different labor intensity
  • Investment, due to different capital intensity
  • Energy consumption, due to different energy intensity
  • Trade balance, due to different propensity to import and export

Example of sectoral decomposition

• The economy is disaggregated into 27 sectors, with in particular:

  • 4 transport sectors
  • 12 energy sectors of which 10 technologies for the production of electricity

• and 23 commodities

  • A commodity can be produced by several sectors. E.g. electricity

• The disaggregation is a compromise between the availability of the national account and energy data and the objective of the model

• Several sectors have to be disaggregated

  • Electricity and gas
  • Transport

Example of sectoral decomposition

Focus on energy

• The energy disaggregation allows for analyzing the energy behavior of economic agents:

  • Sectors can arbitrate between different energy investments:
    • Substitution between capital & energy when the relative energy price increases
    • Substitution between energy sources
    • Substitution between transports
    • Endogenous energy efficiency: technical progress increases when the relative energy price increases
  • Consumers
    • Substitution between capital & energy
    • Substitution between energy sources
    • Substitution between transports
    • Substitution between goods

Type of simulation of the economic and environmental impact

• Energy transition policies

  • Fiscal policies:
    • Carbon tax with or without redistribution of the tax revenue
    • Phasing out subsidies on (fossil fuel) energy
    • Bonus-malus for cars: subsidies on green cars financed by a tax on other cars
  • Change in the electricity production mix
    • Ex: more RES in the mix
  • Impact of green investment
    • In buildings, public transport, etc.
    • Impact of applying a new standard for buildings, or appliances

• External shock

  • Increase in international oil/gas price

CGE model

• Computable: numerical simulation

• General: take into account the interactions between markets.

  • Supply and demand influence each other

• Equilibrium: Supply is equal to demand on all markets (good, production factors)

• Structure of a CGE model (see next Figure):

  • Demand (Consumption, investment) defines the supply (production)
  • Supply defines in return the demand through the incomes generated by the production factors

What does general equilibrium mean?

• General Equilibrium relates to a state where supply is equal to demand in all markets

• 2 main approaches to ensure this state:

  • Walrasian models

    • The equilibrium force is the price system

    • Perfect price flexibility ensures the instantaneous equilibrium between supply and demand

    • When the supply of a commodity goes down, its price tends to go up, thereby stimulating additional supply and depressing demand, until supply and demand are equal again.

    • Static model

  • Neo-Keynesian models
    • Demand determines supply in the short run
    • Supply influances demand in the medium and long term through income distribution and technology
    • Price and quantities are rigid and adjust slowly
    • Disequilibrium between notional (optimal) supply and the actual supply in the short run
    • Dynamic model: transition to the long run

A neo-keynesian CGE model

• Slow adjustment of prices and quantities

  • Adjustment costs
  • Empirically firms adjust their production to the demand rather than their price

• Leads to situation of disequilibrium between the desired supply and demand

• Prices are defined as a mark-up over the firm’s production costs

  • Production costs integrate intermediary consumption (material and energy), labor and capital costs

• Wages are determined by a Wage Setting (WS) curve

  • Phillips curve: wages increase with inflation and decrease with unemployment
  • Wages do not adjust instantaneously the supply and demand for labor:
    • Permanent underemployment equilibrium possible
    • Theory of the NAIRU (Non Accelerating Inflation Rate of Unemployment) or Equilibrium rate of unemployment

• The interest rate does not equilibrate instantaneously saving and investment:

  • It is defined by the Central Bank
  • « Taylor » reaction function: increases with inflation, decreases with unemployment

Key properties of ThreeME

• General equilibrium effects

  • Supply influence demand and vice versa

• Direct and indirect effects of the energy transition

  • Direct effects: impact for the energy sectors
  • Indirect effects: impact for the rest of the economy (in particular the other sectors, the government, households).

• Limited eviction effects

  • Investment is not only defined by saving
  • The financing through bank credit does not necessary lead to an increase of the interest rate
  • The augmentation of investment in one sector is not necessary achieved through a decrease of investment in other sectors

The value-added compared to existing models

• Sectorial disaggregation

  • Make explicit the negative and positive impacts for each sector according to its own specificities.

• High technological disaggregation of the energy system

  • Ex: electricity produced by several technology
  • Each technology having their own cost and production function
  • Link between economic activity, energy production in physical terms (Mtoe or Mwh) and CO2 emissions more accurate.

• General Equilibrium

  • Allows for taking into account of indirect and feedback effects (rebound effects)

• Neo-keynesian features

  • Allows for studying transition and disequilibrium phases (such underemployment) not only the long term

The value-added compared to existing models

• Hybrid modelling

  • Link bottom-up and top-down approaches
  • Detailed energy technologies and coherent macroeconomic framework

• Possibility of combination with an energy system model

  • The bottom-up development of the energy sectors makes it possible to combine ThreeME with an energy system model without loss of relevant information
  • Assessment of scenarios compatible with the technical constraints regarding the feasible energy mix.

Data: Supply-Use (SU) and Input-Output (IO) tables

• SU table says how much a given commodities is supplied by a given sector (Supply)

  • Generally close to a diagonal matrix

• IO table says how much a given commodities is purchased by a given sector (Demand)

  • Not a diagonal matrix

Equilibrium between Supply and Demand (use)

• GDP = VA = Y – CI = C + I + X - M

Adjustment mechanisms

• ThreeME takes into account explicitly the slow adjustment of prices and quantities (factors of production, consumption)

• ThreeME assumes that the actual levels of prices and quantities gradually adjust to their notional level

• The notional level corresponds to the optimal (desired or target) level that the economic agent would choose in the absence of adjustment constraints

• Microeconomic foundation for a slow adjustment process:

  • Adjustment models: Eisner and Strotz (1963) and Gould (1968), Lucas (1967), Schramm (1970) and Treadway (1971), Rotemberg (1982)

  • The adjustment process is derived from an optimal behavior: minimizing an adjustment cost function (Rotemberg,1982)

Adjustment mechanisms

• Adjustment process for prices and quantities:

\[\operatorname{log} X_{t} = \alpha^{{0},X} \; \operatorname{log} X^{n}_{t} + \left( 1 - \alpha^{{0},X} \right) \; \left( \operatorname{log} X_{t-1} + \varDelta \left(\operatorname{log} X^{e}_{t}\right) \right)\]

• Expectations for prices and quantities

  • Mix of adaptative and rational expections (backward forward-looking features):

\[\varDelta \left(\operatorname{log} X^{e}_{t}\right) = \alpha^{{1},X} \; \varDelta \left(\operatorname{log} X^{e}_{t-1}\right) + \alpha^{{2},X}\; \varDelta \left(\operatorname{log} X_{t-1}\right) \\ + \alpha^{{3},X} \; \varDelta \left(\operatorname{log} X^{n}_t\right) + \alpha^{{4},X} \; \varDelta \left(\operatorname{log} X_{t+1}\right)\]

Where \(X_{t}\) is the effective value of a given variable, \(X^{n}_t\) is its notional level, \(X^{e}_t\) its expected (anticipated) value at period \(t\) and \(\alpha^{{i},X}\) are the adjustments parameters, with \(\alpha^{{1},X} + \alpha^{{2},X} + \alpha^{{3},X} + \alpha^{{4},X} = 1\).

Long term properties

• In the long run, ThreeME converges toward a steady state where all variables grow at a constant rate:

  • the model is neo-classical in the sense of Solow (Solow, 1956).
  • all real variables grow at the same rate defined as the sum of the growth rate of the technical progress and of the population.

Neo-Keynesian vs. New Keynesian DSGE models

ThreeME is not a so-called ”new Keynesian” model as defined in the Dynamic Stochastic General Equilibrium (DSGE) literature. In particular, ThreeME does not assume a functioning of the economy with perfect information (about the future) and with perfectly rational and forward-looking agents.

Adjustments: Minimizing an adjustment cost function

• To take into account that the changes in price are all the more costly that they are large propose to use quadratic adjustment cost models (Rotemberg, 1982).
  
• The firm defines the optimal price as a trade-off between the cost of adjusting and the cost of not been adjusted.

\[\begin{equation} \Gamma_t\left(X_t\right)-\Gamma_t\left(X_t^n\right)=\Gamma_t^{\prime}\left(X_t^n\right)\left(X_t-X_t^n\right)+\Gamma_t^{\prime \prime}\left(X_t^n\right)\left(X_t-X_t^n\right)^2 \end{equation}\] The profit being maximum for \(X_t^n, \Gamma_t^{\prime}\left(X_t^n\right)=0\) and \(\Gamma_t^{\prime \prime}\left(X_t^n\right)<0\). As a first approximation, the adjustment cost, i.e. the loss of profit suffered by a company that is not in the optimum, is therefore: \[ C_D=\Gamma_t\left(X_t^n\right)-\Gamma_t\left(X_t\right)=C_D\left(X_t-X_t^n\right)^2 \] Where: \[ C_D=-\Gamma_t^{\prime \prime}\left(X_t^n\right) \] Suppose that the adjustment cost is proportional to the square of the speed of adjustment: \[ C_A=c_A\left(X_t-X_{t-1}\right)^2 \] Where: \[ c_A>0 \] Minimizing the total cost function \(\left(C_t=C_D+C_A\right)\) is equivalent to solving: \[ C_t^{\prime}\left(X_t\right)=2 c_D\left(X_t-X_t^n\right)+2 c_A\left(X_t-X_{t-1}\right)=0 \] The condition of the second order \(\left(C_t^{\prime \prime}\left(X_t\right)>0\right)\) being always verified, the optimal adjustment which minimizes the total cost has the following dynamic process: \[ X_t=\alpha X_t^n+(1-\alpha) X_{t-1} \] With: \[ \alpha=\frac{c_D}{\left(c_D+c_A\right)} \]

With this simple model, the average adjustment time is: \[ \frac{\alpha}{(1-\alpha)}=\frac{c_D}{c_A} \] The slower the adjustment, the higher the adjustment cost \(c_A\) compared to the cost of non being adjusted \(c_D\).

Production of commodities of each sector

• The production of a commodity can be produced by several sectors:

\[Y_{c, s} = \varphi^{Y}_{c, s} \; YQ_{c}\]

• \(YQ_c\) : aggregated domestic production of commodity \(c\). It is determined by the demand (intermediate and final consumption, investment, public spending, exports and stock variation).

• \(PhiY_{c, s}\) : share of commodity \(c\) produced by the sector \(s\) (with \(\sum_{s} phiY_{c,s} =1\))

• Aggregated production of sector \(s\):

\[Y_{s} = \sum_{s} Y_{c, s}\]

Structure of production

Demand for production factors

• Notional production factors demand derived from a production costs minimization program assuming a Variable Output Elasticity (VOE) Cobb–Douglas production function

  • more flexible production function than the CES function: elasticity of substitution can differ between pair of inputs
  • Reynès, F. (2019). The Cobb–Douglas function as a flexible function: A new perspective on homogeneous functions through the lens of output elasticities. Mathematical Social Sciences, 97, 11-17.

\[\varDelta \left(\operatorname{log} F^{n}_{f, s}\right) = \varDelta \left(\operatorname{log} Y_{s}\right) - \varDelta \left(\operatorname{log} PROG_{f, s}\right) + \varDelta \left(SUBST^{F}_{f, s}\right)\]

\[\varDelta \left(SUBST^{F,n}_{f, s}\right) = \sum_{ff} -ES_{f, ff, s} \; \varphi_{ff, s, t-1} \; \varDelta \left(\operatorname{log} \frac{C_{f, s}}{PROG_{f, s}} - \operatorname{log} \frac{C_{ff, s}}{PROG_{ff, s}}\right)\]

• Input (cost) share: \[\varphi_{f, s} = \frac{C_{f, s} \; F^{n}_{f, s}}{\sum_{ff} C_{ff, s} \; F^{n}_{ff, s}}\]
• Notional demand of input \(f\) (\(KLEM\)): \(F_{f,s}^n\)
• Elasticity of substitution (ES) between the pairs of inputs \(f\) and \(ff\): \(ES_{f,ff,s}\)
• Technical progress related to input \(f\): \(PROG_{f,s}\)
• Cost/price of input \(f\): \(C_{f,s}\)
• Production of sector \(s\): \(Y_{s}\)

Investment and capital

• Investment depends:

  • on the anticipated production, on its past dynamic
  • on substitution phenomena
  • on a correction mechanism, which guaranties that the level of notional capital stock is reached in the long-term

\[\varDelta \left(\operatorname{log} IA_{s}\right) = \alpha^{IA,Ye}_{s} \; \varDelta \left(\operatorname{log} Y^{e}_{s}\right) + \alpha^{IA,IA1}_{s} \; \varDelta \left(\operatorname{log} IA_{s, t-1}\right) \\ + \alpha^{IA,SUBST}_{s} \; \varDelta \left(SUBST^{F}_{K, s}\right) \\ + \alpha^{IA,Kn}_{s} \; \left( \operatorname{log} F^{n}_{K, s, t-1} - \operatorname{log} F_{K, s, t-1} \right)\]

• Stock of capital deducted from investment according to the standard capital accumulation equation:

\[F_{K, s} = \left( 1 - \delta_{s} \right) \; F_{K, s, t-1} + IA_{s}\]

Price setting

• The notional production price for each sector is set by applying a mark-up over the unit cost of production

  • Costs include labor, capital, energy and other intermediate consumption costs

\[PY^{n}_{s} = CU^{n}_{s} \; \left( 1 + \mu_{s} \right)\]

Where \(PY^n\) is the notional price, \(CU^n_s\) the unitary cost of production and \(\mu_{s}\) is the mark-up.

• Notional mark-up of each sector depends on the capacity utilization ratio:

\[\varDelta \left(\operatorname{log} \left(1 + \mu^{n}_{s}\right)\right) = \rho^{\mu,Y} . \varDelta \left(\operatorname{log} CUR_{s}\right)\]

• capacity utilization ratio \[CUR_{s} = \frac{Y_{s}}{YCAP_{s}}\]

• Production capacity

\[\varDelta \left(\operatorname{log} YCAP_{s}\right) = \sum_{f} \varphi_{f, s, t-1} \; \varDelta \left(\operatorname{log} \left(F_{f, s} \; PROG_{f, s}\right)\right) \]

Wage setting

• The notional nominal wage (\(W^n_s\)) positively depends on the anticipated consumption price (\(P^e\)) and on the labor productivity (\(PROG^L_s\)), and negatively on the unemployment rate (\(UnR\)):

\[\varDelta \left(\operatorname{log} W^{n}_{s}\right) = \rho^{W,Cons}_{s} + \rho^{W,P}_{s} \; \varDelta \left(\operatorname{log} P\right) + \rho^{W,Pe}_{s} \; \varDelta \left(\operatorname{log} P^{e}\right) \\ + \rho^{W,PROG}_{s} \; \varDelta \left(\operatorname{log} PROG^{L}_{s}\right) - \rho^{W,U}_{s} \; \left( UnR - DNAIRU \right) \\ - \rho^{W,DU}_{s} \; \varDelta \left(UnR\right) + \rho^{W,L}_{s} \; \varDelta \left(\operatorname{log} F_{L, s} - \operatorname{log} F_{L}\right)\]

• General specification that includes the Phillips and Wage Setting (WS) curves depending on the value of the selected parameters (Heyer et al., 2007; Reynès, 2010)

  • Phillips curve if \(\rho^{W,U}_{s}\neq 0\)
  • WS curve if \(\rho^{W,U}_{s} = 0\)
    • Constraints of the specification proposed by Layard et al.
      • Unitary indexation of wages on inflation ( \(\rho^{W,P}_{s}+\rho^{W,Pe}_{s}=1\)), and on labor productivity (\(\rho^{W,PROG}_{s}=1\))
      • \(\rho^{W,Cons}_{s}=0\)

Interest rate

• In the neo-Keynesian framework, it is standard to assume that the interest rate is set by the Central Bank (CB) according to a Taylor rule (Taylor, 1993).

• The CB maximizes an objective function by making a trade-off between inflation and economic activity (unemployment)

• The real interest rate is

  • a positive function of inflation
  • a negative function of the unemployment rate (proxi of the output gap)

\[\varDelta \left(R^{n}\right) = \rho^{Rn,P} . \varDelta \left(\frac{\varDelta \left(P\right)}{P_{t-1}}\right) - \rho^{Rn,UnR} . \varDelta \left(UnR\right)\]

Aggregate households’ consumption

• The notional (optimal) aggregate households consumption corresponds to a share of their current income:

\[CH^{n,VAL} = DISPINC^{AT,VAL} . \left( 1 - MPS^{n} \right)\]

Where \(CH^{n,VAL}\) is the aggregate notional households final consumption expressed in value, \(DISPINC^{AT,VAL}\) is the households’ disposable income - The notional marginal propensity to save (\(MPS^n\) their ) depends on the real interest rate and on the unemployment rate:

\[\varDelta \left(MPS^{n}\right) = \rho^{MPS,R} . \varDelta \left(R - \frac{\varDelta \left(P\right)}{P_{t-1}}\right) + \rho^{MPS,UnR} . \varDelta \left(UnR\right)\]

Households’ consumption per commodity

ThreeME includes three model variants for the allocation of the aggregate consumption between the different commodities:

• Variant 1: LES utility function
• Variant 2: Nested utility function
• Variant 3: Hybrid approach

Variant 1: LES utility function

• In the standard version of the model, consumption decisions between commodities are modeled through a Linear Expenditure System (LES) utility function generalized to the case of a non-unitary elasticity of substitution between the commodities (Brown and Heien, 1972).

• A LES specification assumes that a share of the base year consumption (\(NCH_c\)) is incompressible: the relation between income and consumption is not linear

• This specification allows for the distinction between the consumption of necessity and luxurious goods

• Notional consumption of commodity \(c\): \[\left( CH^{n}_{c} - NCH_{c} \right) \; PCH_{c} = \varphi^{MCH}_{c} \; \left( CH^{n,VAL} - PNCH . NCH \right)\]

• Share of consumption of commodity \(c\):

\[\varDelta \left(\operatorname{log} \varphi^{MCH}_{c}\right) = \left( 1 - \eta^{LESCES} \right) . \varDelta \left(\operatorname{log} \frac{PCH_{c}}{PCH^{CES}}\right)\]

• CES consumer price index:

\[PCH^{CES} = \left( \sum_{c} \varphi^{MCH}_{c, t_0} \; PCH_{c} ^ {\left( 1 - \eta^{LESCES} \right)} \right) ^ {\left( \frac{1}{\left( 1 - \eta^{LESCES} \right)} \right)}\]

Variant 2: Nested utility function

Variant 3: Hybrid approach

• Calibrated for the French version of ThreeME
• Bottom-up modeling of the stock of buildings and automobiles per energy label and type of fuel

Foreign trade

• Exports are determined by the external demand addressed to domestic products and the ratio between the export and world prices:

\[\varDelta \left(\operatorname{log} X_{c}\right) = \varDelta \left(\operatorname{log} WD_{c}\right) + \varDelta \left(SUBST^{X}_{c}\right)\]

\[\varDelta \left(SUBST^{X,n}_{c}\right) = -\eta^{X}_{c} \; \varDelta \left(\operatorname{log} PX_{c} - \operatorname{log} \left(EXR . PWD_{c}\right)\right)\]

Where \(WD_{c}\) is the world demand, \(PWD_{c}\) its price. \(PX_{c}\) is the export price that depends on the production costs and which reflects the price-competitiveness of the domestic products. \(EXR\) is the exchange rate; \(\sigma^{X}_{c}\) is the price-elasticity (assumed constant).

• Imports are modeled per use (intermediate consumption per commodity and sector, households consumption, investment, public expenditure)
• We assume imperfect substitution between domestic and imported goods (Armington, 1969)
• Demand for domestic and imported products of use \(A\):

\[AM_{c} = \varphi^{AM}_{c} \; A_{c}\]

\[AD_{c} = \left( 1 - \varphi^{AM}_{c} \right) \; A_{c}\]

• Import share for use \(A\):

\[\varphi^{AM}_{c} = \frac{1}{\left( 1 + \frac{AD_{c}}{AM_{c}, t_0} \; \operatorname{exp} SUBST^{AM}_{c} \right)}\] \[\varDelta \left(SUBST^{AM,n}_{c}\right) = -\sigma^{AM}_{c} \; \varDelta \left(\operatorname{log} PAD_{c} - \operatorname{log} PAM_{c}\right)\]

\[SUBST^{AM}_{c} = \alpha^{{6},AM}_{c} \; SUBST^{AM,n}_{c} + \left( 1 - \alpha^{{6},AM}_{c} \right) \; SUBST^{AM}_{c, t-1}\]

Government

• According to the national accounts, public administrations generally refer to the central and regional government services and social security administration.
• In ThreeME, three components are aggregated in order to focus on transfers between public administrations, household and sectors.

Government’s resources (\(INC^{G,VAL}\)) :

\[INC^{G,VAL} = PNTAXC . NTAXC + NTAXS^{VAL} + INC^{SOC,TAX,VAL} \\ + PRSC . RSC + PROP^{INC,G,VAL}\]

with:

• The aggregate net taxes on commodity \(c\) expressed in value: \(PNTAXC.NTAXC\)
• The aggregate net taxes on production of sectors expressed in value: \(NTAXS^VAL\)
• The income and social taxes expressed in value: \(INS^{SOC,TAX,VAL}\)
• The aggregate employers’ social security contribution paid by sector: \(PRSC.RSC\)
• The property income of the Government expressed in value: \(PROP^{INC,G,VAL}\)

Government’s expenditures (\(SPEND^{G,VAL}\)):

\[SPEND^{G,VAL} = PG . G + SOC^{BENF,VAL} + DEBT^{G,VAL}_{t-1} \; \left( \varphi^{RD^{G}}_{t-1} + r^{DEBT,G}_{t-1} \right)\]

with:

• The government final consumption: \(PG.G\)
• The Social benefits expressed in value: \(SOC^{BENF,VAL}\)
• The interest paid by the government on its debt plus the share of debt reimbursed every year: \(DEBT^{G,VAL}_{t-1}\left(\varphi^{RD^G}_{t-1} + r^{DEBT,G}_{t-1}\right)\)

Greenhouse gases emissions

• Energy consumption detailed by economic agents (households and economic sectors) for each energy source (coal, oil, gas, electricity).
• This allows for simulating GHG emissions per agents and per energy source
• The calculation of emissions level consists in multiplying the fossil energy demand by the corresponding emission coefficients. These coefficients are specific for each economic actor, each sector and each energy sources depending on their carbon intensity.

Emissions of the greenhouse gas \(ghg\) related to the intermediary consumption of commodity \(c\) by sector \(s\)

\[\varDelta \left(\operatorname{log} EMS^{CI}_{ghg, c, s}\right) = \varDelta \left(\operatorname{log} \left(CI_{c, s} \; IEMS^{CI}_{ghg, c, s}\right)\right)\]

where \(IEMS^{CI}_{ghg, c, s}\) is the corresponding emission intensity calibrated to 1 in the base year. It may change over time because of the increase of the share of biofuels.

Emissions of the greenhouse gas \(ghg\) related to the household consumption \(c\)

\[\varDelta \left(\operatorname{log} EMS^{CH}_{ghg, c}\right) = \varDelta \left(\operatorname{log} \left(CH_{c} \; IEMS^{CH}_{ghg, c}\right)\right)\]

Emissions of the greenhouse gas \(ghg\) related to the final production of sector \(s\)

\[\varDelta \left(\operatorname{log} EMS^{Y}_{ghg, s}\right) = \varDelta \left(\operatorname{log} \left(Y_{s} \; IEMS^{Y}_{ghg, s}\right)\right)\]

Emissions of the greenhouse gas \(ghg\) related to the materials consumption of sector \(s\)

\[\begin{equation} \small \varDelta \left(\operatorname{log} EMS^{MAT}_{ghg, s}\right) = \varDelta \left(\operatorname{log} \left(F_{MAT, s} \; IEMS^{MAT}_{ghg, s}\right)\right) \end{equation}\]

\(CO_2\) emissions from decarbonation during the production process for the non mineral metallic products, as the glass or ceramic sectors, is assumed proportional to the quantity of intermediate raw material used in the production process.

Energy balance

• The energy demand is segmented by type of end use between intermediate consumption \((CI_{toe})\), households final consumption \((CH_{toe})\) and exports \((X_{toe})\):

\[\varDelta \left(\operatorname{log} CI^{toe}_{ce, s}\right) = \varDelta \left(\operatorname{log} CI_{ce, s}\right)\]

• The net energy supply equals energy use and is consistent with the national account concept of production, that is the physical quantity actually bought by the end user:

\[Y^{toe}_{ce} + M^{toe}_{ce} = CI^{toe}_{ce} + CH^{toe}_{ce} + X^{toe}_{ce}\]

• Each sector \(s\) produces a share of energy \(ce\)

\[Y^{toe}_{ce, s} = \varphi^{Y^{toe}}_{ce, s} \; Y^{toe}_{ce}\] where \(\varphi_{ce,s}^{Y^{toe}}\) is the share energy \(ce\) produced by sector \(s\)

• Share of energy \(ce\) produced by sector \(s\) (monetary definition):

\[\varphi^{Y}_{ce, s} = \frac{PY^{toe}_{ce, s, t_0} \; \varphi^{Y^{toe}}_{ce, s}}{\sum_{ss} \left( PY^{toe}_{ce, ss, t_0} \; \varphi^{Y^{toe}}_{ce, ss} \right)}\]